Three men deported by the US to Eswatini – rather than their home countries – have filed a case against Eswatini’s government with the African Union’s human rights body, claiming their detention was an unlawful violation of their rights.

Two of the claimants, from Cuba and Yemen, have been in prison in Eswatini, formerly Swaziland, for eight months. The third, Orville Etoria, was repatriated to his home country, Jamaica, in September.

They were among a group of five men deported by the US in July, with another 10 sent in October. Other than Etoria, all remained in prison in Eswatini, their lawyers said. The US has labelled the men dangerous criminals but their lawyers said they have already served their sentences for any crimes committed in the US.

The men’s complaint was filed with the African Commission on Human and Peoples’ Rights (ACHPR), an African Union body that monitors member states’ compliance with regional human rights agreements. The commission can demand that states uphold rights and refer cases to the African court on human and peoples’ rights, but neither body has enforcement powers.

Beatrice Njeri, a lawyer with the Global Strategic Litigation Council, one of the organisations that brought the case on the deportees’ behalf, said: “The people in detention have committed no crime [in Eswatini] and continue to undergo various human rights violations … They are being held indefinitely.”

Njeri said the men had still not been allowed to see their lawyers in person. She said one detainee had gone on a 30-day hunger strike late last year, resulting in signs of organ failure. “They’re totally frustrated with the situation,” she said. “They just want to go back – some of them home, some of them to the US”.

Thabile Mdluli, a spokesperson for Eswatini’s government, said she had not seen the legal complaint.

The US has deported dozens of immigrants to third countries, as Donald Trump’s administration attempts to carry out mass deportations. US Immigration and Customs Enforcement (ICE) has detained more than 68,000 people in the US.

Other African countries that have accepted third-country deportees from the US include Ghana, Rwanda, South Sudan and Uganda. The US agreed to pay Eswatini $5.1m to take up to 160 third-country nationals, according to Reuters.

In February, Eswatini’s high court threw out a case from local NGOs that had argued the government’s imprisonment of the deportees was unconstitutional. The court ruled that the applicants had no right to bring the legal challenge, as they did not have a direct interest in the matter.